One of the major challenges in large scale optical imaging of neuronal activity is to simultaneously achieve sufficient temporal and spatial resolution across a large volume. Here, we introduce sparse decomposition light-field microscopy (SDLFM), a computational imaging technique based on light-field microscopy (LFM) that takes algorithmic advantage of the high temporal resolution of LFM and the inherent temporal sparsity of spikes to improve effective spatial resolution and signal-to-noise ratios (SNRs). With increased effective spatial resolution and SNRs, neuronal activity at the single-cell level can be recovered over a large volume. We demonstrate the single-cell imaging capability of SDLFM with in vivo imaging of neuronal activity of whole brains of larval zebrafish with estimated lateral and axial resolutions of similar to 3.5 mu m and similar to 7.4 mu m, respectively, acquired at volumetric imaging rates up to 50 Hz. We also show that SDLFM increases the quality of neural imaging in adult fruit flies.